FL AP Calculus AB BC Demana Calculus 2016

A Correlation of

Calculus

Graphical, Numerical, Algebraic 5e AP? Edition, ?2016

Finney, Demana, Waits, Kennedy, & Bressoud

to the

Florida Advanced Placement Calculus AB/BC Standards

(#1202310 & #1202320)

AP? is a trademark registered and/or owned by the College Board, which was not involved in the production of, and does not endorse, this product.

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

Math Practices MPAC 1: Reasoning with definitions and theorems

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

Reasoning with definitions and theorems is one of the dominant themes in the development of each new idea and of the exercises. Definitions and theorems are highlighted in each section and summarized at the end of each chapter for reference and review.

MPAC 2: Connecting concepts

Connecting concepts runs throughout this book, introducing new concepts by

connecting them to what has come before and in the reliance of many exercises that

draw on applications or build on student knowledge. Quick Review exercises at the

start of each Exercise set review concepts

from previous sections (or previous courses) that will be needed for the solutions.

MPAC 3: Implementing algebraic/computational processes

Implementing algebraic/computational processes is well represented in the

foundational exercises with which each exercise set begins and in the thoughtful use

of technology.

MPAC 4: Connecting multiple representations

Connecting multiple representations has

always been present in the emphasis on the connections among graphical, numerical,

and algebraic representations of the key concepts of calculus. The title of this book

speaks for itself in that regard.

MPAC 5: Building notational fluency

Building notational fluency is represented in

the intentional use of a variety of notational

forms and in their explicit connection to graphical, numerical, and algebraic

representations. Many margin notes explicitly address notational concerns.

MPAC 6: Communicating

Communicating is a critical component of the Explorations that appear in each section.

Communication is also essential to the Writing to Learn exercises as well as the

Group Activities. Many of the exercises and examples in the book have "justify your

answer" components in the spirit of the AP

exams.

1 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

Big Idea 1: Limits

EU 1.1: The concept of a limit can be used to understand the behavior of functions.

LO 1.1A(a): Express limits symbolically using SE/TE: 2.1 Rates of Change and Limits,

correct notation.

2.2 Limits Involving Infinity

LO 1.1A(b): Interpret limits expressed symbolically.

SE/TE: 2.1 Rates of Change and Limits, 2.2 Limits Involving Infinity

LO 1.1B: Estimate limits of functions.

SE/TE: 2.1 Rates of Change and Limits, 2.2 Limits Involving Infinity

LO 1.1C: Determine limits of functions.

SE/TE: 2.1 Rates of Change and Limits, 2.2 Limits Involving Infinity, 9.2

L'Hospital's Rule, 9.3 Relative Rates of Growth

LO 1.1D: Deduce and interpret behavior of functions using limits.

SE/TE: 2.1 Rates of Change and Limits, 2.2 Limits Involving Infinity, 9.3 Relative

Rates of Growth

EU 1.2: Continuity is a key property of functions that is defined using limits.

LO 1.2A: Analyze functions for intervals of

SE/TE: 2.3 Continuity

continuity or points of discontinuity.

LO 1.2B: Determine the applicability of

important calculus theorems using continuity.

SE/TE: 2.3 Continuity, 5.1 Extreme Values

of Functions, 5.2 Mean Value Theorem, 6.2 Definite Integrals, 6.3 Definite Integrals

and Antiderivatives, 6.4 Fundamental

Theorem of Calculus

Big Idea 2: Derivatives

EU 2.1: The derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies.

LO 2.1A: Identify the derivative of a function SE/TE: 3.1 Derivative of a Function as the limit of a difference quotient.

LO 2.1B: Estimate the derivative.

SE/TE: 3.1 Derivative of a Function, 3.2 Differentiability

LO 2.1C: Calculate derivatives.

SE/TE: 3.3 Rules for Differentiation,

3.5 Derivatives of Trigonometric Functions, 4.1 Chain Rule, 4.2 Implicit Differentiation,

4.3 Derivatives of Inverse Trigonometric

Functions, 4.4 Derivatives of Exponential and Logarithmic Functions, 11.1 Parametric

Functions, 11.2 Vectors in the Plane, 11.3 Polar Functions

2 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

LO 2.1D: Determine higher order derivatives.

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

SE/TE: 3.3 Rules for Differentiation, 4.2 Implicit Differentiation

EU 2.2: A function's derivative, which is itself SE/TE: 2.4 Rates of Change, Tangent Lines,

a function, can be used to understand the

and Sensitivity

behavior of the function.

LO 2.2A: Use derivatives to analyze properties of a function.

SE/TE: 5.1 Extreme Values of Functions,

5.2 Mean Value Theorem, 5.3 Connecting f' and f" with the Graph of f, 11.1 Parametric

Functions, 11.2 Vectors in the Plane, 11.3 Polar Functions

LO 2.2B: Recognize the connection between SE/TE: 3.2 Differentiability differentiability and continuity.

EU 2.3: The derivative has multiple interpretations and applications including those that

involve instantaneous rates of change.

LO 2.3A: Interpret the meaning of a

SE/TE: 2.4 Rates of Change, Tangent Lines,

derivative within a problem.

and Sensitivity, 3.1 Derivative of a Function,

3.4 Velocity and Other Rates of Change,

5.5 Linearization, Sensitivity, and

Differentials

LO 2.3B: Solve problems involving the slope of a tangent line.

SE/TE: 2.4 Rates of Change, Tangent Lines, 3.4 Velocity and Other Rates of Change,

5.5 Linearization, Sensitivity, and

Differentials

LO 2.3C: Solve problems involving related

rates, optimization, rectilinear motion, (BC) and planar motion.

SE/TE: 3.4 Velocity and Other Rates of

Change, 5.1 Extreme Values of Functions, 5.3 Connecting f' and f" with the Graph of f,

5.4 Modeling and Optimization, 5.6 Related Rates, 11.1 Parametric Functions, 11.2

Vectors in the Plane, 11.3 Polar Functions

LO 2.3D: Solve problems involving rates of change in applied contexts.

LO 2.3E: Verify solutions to differential equations.

LO 2.3F: Estimate solutions to differential equations.

SE/TE: 5.5 Linearization, Sensitivity, and Differentials, 5.6 Related Rates SE/TE: 7.1 Slope Fields and Euler's Method

SE/TE: 7.1 Slope Fields and Euler's Method

3 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

EU 2.4: The Mean Value Theorem connects the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval.

LO 2.4A: Apply the Mean Value Theorem to SE/TE: 5.2 Mean Value Theorem describe the behavior of a function over an interval.

Big Idea 3: Integrals and the Fundamental Theorem of Calculus

EU 3.1: Antidifferentiation is the inverse process of differentiation.

LO 3.1A: Recognize antiderivatives of basic SE/TE: 6.3 Definite Integrals and

functions.

Antiderivatives

EU 3.2: The definite integral of a function over an interval is the limit of a Riemann sum

over that interval and can be calculated using a variety of strategies.

LO 3.2A(a): Interpret the definite integral as SE/TE: 6.1 Estimating with Finite Sums,

the limit of a Riemann sum.

6.2 Definite Integrals

LO 3.2A(b): Express the limit of a Riemann sum in integral notation.

LO 3.2B: Approximate a definite integral.

LO 3.2C: Calculate a definite integral using areas and properties of definite integrals.

SE/TE: 6.2 Definite Integrals

SE/TE: 6.1 Estimating with Finite Sums, 6.2 Definite Integrals, 6.5 Trapezoidal Rule

SE/TE: 6.2 Definite Integrals, 6.3 Definite Integrals and Antiderivatives

LO 3.2D: (BC) Evaluate an improper integral SE/TE: 9.4 Improper Integrals or show that an improper integral diverges.

EU 3.3: The Fundamental Theorem of Calculus, which has two distinct formulations,

connects differentiation and integration.

LO 3.3A: Analyze functions defined by an

SE/TE: 6.1 Estimating with Finite Sums,

integral.

6.2 Definite Integrals, 6.3 Definite Integrals

and Antiderivatives, 6.4 Fundamental

Theorem of Calculus, 8.1 Accumulation and

Net Change

LO 3.3B(a): Calculate antiderivatives.

SE/TE: 6.3 Definite Integrals and Antiderivatives, 6.4 Fundamental Theorem

of Calculus, 7.2 Antidifferentiation by Substitution, 7.3 Antidifferentiation by Parts,

7.5 Logistic Growth

4 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

LO 3.3B(b): Evaluate definite integrals.

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

SE/TE: 6.3 Definite Integrals and Antiderivatives, 6.4 Fundamental Theorem of Calculus, 7.2 Antidifferentiation by Substitution, 7.3 Antidifferentiation by Parts, 7.5 Logistic Growth

EU 3.4: The definite integral of a function over an interval is a mathematical tool with many

interpretations and applications involving accumulation.

LO 3.4A: Interpret the meaning of a definite SE/TE: 6.1 Estimating with Finite Sums,

integral within a problem.

6.2 Definite Integrals, 8.1 Accumulation and

Net Change, 8.5 Applications from Science

and Statistics

LO 3.4B: Apply definite integrals to problems SE/TE: 6.3 Definite Integrals and

involving the average value of a function.

Antiderivatives

LO 3.4C: Apply definite integrals to problems involving motion.

SE/TE: 6.1 Estimating with Finite Sums,

8.1 Accumulation and Net Change, 11.1 Parametric Functions, 11.2 Vectors in

the Plane, 11.3 Polar Functions

LO 3.4D: Apply definite integrals to problems involving area, volume, (BC) and length of a curve.

LO 3.4E: Use the definite integral to solve problems in various contexts.

SE/TE: 8.2 Areas in the Plane, 8.3 Volumes, 8.4 Lengths of Curves

SE/TE: 6.1 Estimating with Finite Sums, .1 Accumulation and Net Change, 8.5 Applications from Science and Statistics

EU 3.5: Antidifferentiation is an underlying concept involved in solving separable differential equations. Solving separable differential equations involves determining a function or relation given its rate of change.

LO 3.5A: Analyze differential equations to obtain general solutions.

SE/TE: 7.1 Slope Fields and Euler's Method, 7.4 Exponential Growth and Decay, 7.5

Logistic Growth

LO 3.5B: Interpret, create, and solve

differential equations from problems in context.

SE/TE: 7.1 Slope Fields and Euler's Method,

7.4 Exponential Growth and Decay, 7.5 Logistic Growth

5 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

A Correlation of Calculus Graphical, Numerical, Algebraic AP Edition, ?2016 to the Advanced Placement Calculus AB/BC Standards

AP Calculus AB / BC Curriculum Framework

Calculus Graphical, Numerical, Algebraic, ?2016

Section References

Big Idea 4: Series (BC)

EU 4.1: The sum of an infinite number of real numbers may converge.

LO 4.1A Determine whether a series

SE/TE: 9.1 Sequences, 10.1 Power Series,

converges or diverges.

10.4 Radius of Convergence, 10.5 Testing

Convergence at Endpoints

LO 4.1B: Determine or estimate the sum of a series.

SE/TE: 10.1 Power Series

EU 4.2: A function can be represented by an associated power series over the interval of

convergence for the power series.

LO 4.2A: Construct and use Taylor

SE/TE: 10.2 Taylor Series, 10.3 Taylor's

polynomials.

Theorem

LO 4.2B: Write a power series representing a SE/TE: 10.1 Power Series, 10.2 Taylor

given function.

Series, 10.3 Taylor's Theorem

LO 4.2C: Determine the radius and interval of convergence of a power series.

SE/TE: 10.4 Radius of Convergence, 10.5 Testing Convergence at Endpoints

6 EU = Enduring Understanding, LO = Learning Objective, BC only topics

SE = Student Edition, TE = Teacher's Edition

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